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Analysis of a case control study (was st: more cases than controls)


From   Philip Ryan <philip.ryan@adelaide.edu.au>
To   statalist@hsphsun2.harvard.edu
Subject   Analysis of a case control study (was st: more cases than controls)
Date   Wed, 24 Mar 2004 17:40:18 +1030

Ricardo

I do not mean to imply that the studies (of which I know nothing!) are *incorrectly* analysed.

Indeed, Hosmer and Lemeshow (Applied Logistic Regression, Wiley 1989) state that, in the univariate case at least, the t test is equivalent to the simple logistic model. They appeal to the analogous discriminant function. This is somewhat qualified by their statements (p84 of first edition):

1. "the most desirable univariate analysis involves fitting a univariate logistic regression..."
2. there are assumptions of normality when using the t test that are not required in the logistic model (I note you appear to have taken care of this)

and

3. ".. the t test should be useful in determining if the variable should be included in the model....", by which they mean a logistic model. That is to say, they certainly don't push the t test as being the test of choice for the c-c study *because the usual objective is to estimate risk* (or some related metric eg OR).

There is no reference in Schlesselman's book "Case Control Studies" (nor in Breslow and Day, nor in Rothman & Greenland's Modern Epidemiology) to the use of the t test in analysis of case control studies, possibly because (i) as I have said before, it seems to reverse the sense of the study design and (ii) it doesn't deliver the risk estimate.

So, I don't think you have analysed _incorrectly_, as long as your analyses are univariate. My own preference (prejudice, practice and pedagogy) is to put predictors on the right and outcomes on the left.

Phil



At 08:01 PM 23/03/2004 -0800, you wrote:

I am now very confused by your intuitive argument.

This was a population-based Case­Control Study
comparing a specific enzyme in the serum of infected
patients (cases) to that in healthy non-infected
controls. We compared these levels using a t-test
after log-tranforming the data. Is this
incorrect?There are many similar studies in the
literature. Am I to understand that they are all
incorrectly analyzed?

Am sorry but I do not get it.

Ricardo.


--- Philip Ryan <philip.ryan@adelaide.edu.au> wrote:
> Ricardo
>
> Leaving aside the question of relative numbers of
> cases and controls, I
> wonder if the reviewers remarked on your choice of
> analysis.  That is to
> say, in a case control study the outcome is the case
> control status, not
> the antecedent exposure (in your study the biomarker
> level).  A t-test
> reverses this sense of the study design, as the
> exposure is now the outcome
> and the case control status is (I was taught) forced
> unnaturally to be the
> "predictor".  In modelling terms, keep the outcome
> defined by the study
> design on the left hand side.  I would choose a
> logistic model, either
> keeping the biomarker level continuous if you
> believe there is a linear
> dose response with the log odds or perhaps with
> dummies of ordered
> categories of the biomarker if you wish to explore
> the functional nature of
> the relationship.
>
> Phil
>
>
>
>
> At 05:32 AM 23/03/2004 -0800, you wrote:
> >Thank you Michel,
> >
> >I would like to clarify two points:
> >
> >1. We had more cases than controls because of
> >budgetary constrains. It was easier and less
> expensive
> >to enroll cases than controls.
> >
> >2. The main outcome of interest was a serum
> biomarker
> >measured on a continuous scale and log transformed
> for
> >the analysis. A t-test was used to compare cases
> and
> >controls and therefore no OR computed.
> >
> >Best,
> >Ricardo.
> >
> >
> >
> >--- Michel Camus <mcamus@videotron.ca> wrote:
> > > Ricardo Ovaldia wrote:
> > >
> > > >(...) We recently submitted a manuscript for
> > > publication to
> > > >a major medical journal. It was a case-control
> > > study
> > > >with 329 cases and 126 controls. One of the
> > > reviewers
> > > >wrote that "to have such a larger number of
> cases
> > > was
> > > >statistically atypical" and asked if the
> "authors
> > > find
> > > >that the use of the same control for multiple
> > > patients
> > > >significantly limits results"?
> > > >
> > > >I never heard of any biases or other problems
> cause
> > > by
> > > >having more cases than controls in a study. We
> had
> > > >sufficient power and the difference for our
> main
> > > >outcome was highly significant (less than
> 0.00001).
> > > Am
> > > >I missing something or is it that this reviewer
> > > does
> > > >not understand the case-control designed? By
> the
> > > way
> > > >this was not a matched study design.
> > > >Thank you,
> > > >Ricardo.
> > > >
> > > >
> > > Dear Ricardo,
> > > There is no problem per se with having less
> controls
> > > than cases, though
> > > it should raise some eyebrows.
> > > The critique of using "the same control for
> multiple
> > > patients" suggests
> > > the reviewer's misunderstanding of an unmatched
> > > design.
> > > A smaller number of controls for a single group
> of
> > > cases is "atypical"
> > > still.
> > > One usually chooses an equal or larger group of
> > > controls to increase
> > > power to be able to detect even a small odds
> ratio
> > > when exposure is
> > > relatively rare.
> > > A smaller number of controls than cases suggests
> > > that the investigators
> > > had more cases than needed given an expected a
> > > priori a large relative
> > > risk (>5) and a high prevalence of exposure
> (>75%)
> > > among controls (cf.
> > > Schlesselmann, 1982, p.155). Could it not then
> be
> > > construed that the
> > > investigators knew enough beforehand not to do a
> > > study?...
> > > With respect to the outcome measure, I do not
> > > understand how you can say
> > > from a case-control study that "the difference
> for
> > > our main outcome was
> > > highly significant (less than 0.00001)".
> Usually
> > > the measure of effect
> > > in a case-control study is an odds ratio, not a
> > > difference (in rates?).
> > >
> > > Michel
> > >
> > > ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
> ~ ~
> > > ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
> > > ~ ~ ~ ~ ~
> > >
> > > Michel Camus, Ph.D.
> > >
> > > Épidémiologue, Div. Biostatistique et
> épidémiologie,
> > > DGSESC, Santé Canada
> > >
> > > Epidemiologist, Biostatistics and Epidemiology
> Div.,
> > > HECSB, Health Canada
> > >
> > > Courriel / e-mail : mcamus@videotron.ca
> > > <mailto:mcamus@videotron.ca>
> > >
> > > Téléphone / phone     :    (514) 850-0157
> > >
> > > Télécopieur / fax        :    (514) 850-0836
> > >
> > > ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
> ~ ~
> > > ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
> > > ~ ~ ~ ~ ~
> > > ==============================
> > >
> > >
> > >
> > >
> > > *
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> Philip Ryan
> Associate Professor,
> Department of Public Health
> Associate Dean (Information Technology)
> Faculty of Health Sciences
> University of Adelaide 5005
> South Australia
> tel 61 8 8303 3570
> fax 61 8 8223 4075
> http://www.public-health.adelaide.edu.au/
> CRICOS Provider Number 00123M
>
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Philip Ryan
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Department of Public Health
Associate Dean (Information Technology)
Faculty of Health Sciences
University of Adelaide 5005
South Australia
tel 61 8 8303 3570
fax 61 8 8223 4075
http://www.public-health.adelaide.edu.au/
CRICOS Provider Number 00123M
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